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Review Sheet: Chapter One & Two Jingrun Chen

Summary: Review Sheet: Chapter One & Two
Jingrun Chen
Math 3C, Spring 2011
Modeling (Single Differential Equation): Malthus Model for Popula-
tion Growth & Saving (Growth Equation), Newton's Law of Cooling &
Radioactive Decay (Decay Equation), Saving & Mixing (Nonhomoge-
neous Equation), Logistic Equation & Threshold Equation (Nonlinear
Autonomous Differential Equation)
Modeling (System of Differential Equations): Predator-Prey Model &
Competition Model (Autonomous System)
Characterize Differential Equations : Single vs. System, Linear vs.
Nonlinear, Order, Homogeneous vs. Nonhomogeneous, Autonomous
vs. Non-autonomous, Separable vs. Nonseparable
Qualitatively Analysis (Single Differential Equation): Direction Fields,
Stability of Equilibria, Bifurcation Diagram
Qualitatively Analysis (System of Differential Equations): Phase Por-
traits, Stability of Equilibria (Not Covered in 3C)
Quantitative Analysis (Single Differential Equation): Explicit Solu-
tion, e.g., Separation of Variables & Integrating Factor Method (Euler-


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics